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A299019 Expansion of Product_{k>=1} (1 - x^k)^(k+1). 1
1, -2, -2, 2, 3, 6, -1, -2, -10, -14, -7, -2, 11, 26, 43, 30, 28, -6, -40, -92, -128, -132, -115, -48, 54, 200, 339, 484, 499, 476, 274, -32, -501, -998, -1539, -1924, -2042, -1838, -1139, 12, 1664, 3540, 5588, 7258, 8392, 8230, 6812, 3480, -1472, -8150, -15737, -23670, -30478 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Convolution of A010815 and A073592.

Convolution inverse of A005380.

LINKS

Table of n, a(n) for n=0..52.

FORMULA

G.f.: exp(-Sum_{k>=1} (sigma_1(k) + sigma_2(k))*x^k/k).

MATHEMATICA

nmax = 52; CoefficientList[Series[Product[(1 - x^k)^(k + 1), {k, 1, nmax}], {x, 0, nmax}], x]

nmax = 52; CoefficientList[Series[Exp[-Sum[(DivisorSigma[1, k] + DivisorSigma[2, k]) x^k/k, {k, 1, nmax}]], {x, 0, nmax}], x]

a[n_] := a[n] = If[n == 0, 1, -Sum[Sum[d (d + 1), {d, Divisors[k]}] a[n - k], {k, 1, n}]/n]; Table[a[n], {n, 0, 52}]

CROSSREFS

Cf. A005380, A010815, A073592, A092346.

Sequence in context: A121256 A022867 A268595 * A070610 A156820 A104346

Adjacent sequences:  A299016 A299017 A299018 * A299020 A299021 A299022

KEYWORD

sign

AUTHOR

Ilya Gutkovskiy, Aug 11 2018

STATUS

approved

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Last modified June 13 11:33 EDT 2021. Contains 344990 sequences. (Running on oeis4.)